上手 and 得意: demonstrated skill and personal strengths
Compare an evaluation of skill with an area of confidence, including subjects, particles, and self-descriptions.
A skillful performance
姉は料理が上手です。 says that the older sister is a good cook. 上手, read じょうず, evaluates skill, with が marking the area of ability.
彼は初めての道具を上手に使いました。 says that he skillfully used a tool new to him. 上手に modifies the actual action without specifying how long he has practiced.
An area of confidence
私は数字を覚えるのが得意です。 says that the speaker is good at remembering numbers. 得意, read とくい, fits introducing an area of strength or confidence.
得意な料理はカレーです。 names curry as the speaker's specialty. Use 得意な before the noun; this does not claim equal skill at every dish.
Self-evaluation and liking
私は料理が得意です naturally presents cooking as a personal strength. 私は料理が上手です is also grammatical, though its direct self-praise can sound different depending on context.
好きですが、まだ上手ではありません。 means that the speaker likes it but is not yet good at it. Liking something and being skilled at it are different.
Does 好きです necessarily imply 上手です?
Show the answer and why
No. A person can like something while still being unskilled. Liking is a preference; 上手 evaluates skill.